The Scottish champions have spent most of the season as the pace-setters in the title race but now find themselves heading into the new year trailing Celtic by two points.
Rangers commanded a 15-point advantage at the summit as recently as early November but a 1-0 defeat in Wednesday’s Old Firm derby means they have now been replaced in pole position by the Hoops.
The Light Blues are now hoping to avoid a third consecutive defeat when they host Motherwell today, having also lost to St Mirren on Christmas Eve.
McCoist said: “That’s the one thing we won’t do, there is absolutely no panic.
“I didn’t think there was an awful lot in the Old Firm game. We lost 1-0 and that can happen.
“In the St Mirren game, whether we like it or not, the sending off had a bearing on the game.
“Both of those games are history now and we have to look forward.
“That’s what we’ve had to do at this club for a number of years, we have to bounce back after disappointments. We will do that again.”
McCoist urged his players to use the visit of the Steelmen to resurrect their title bid.
He said: “We all have to pull together. We have had a disappointing couple of weeks but we have to be very positive and we will be positive.
“I felt we were positive in the game on Wednesday. We set out a very positive side.
“In saying that, we should have created more chances than we did and we didn’t work the Celtic goalkeeper enough.
“But we’ve certainly got positive players and we have positive thoughts as a coaching staff and that will have to be very important in the coming weeks.”
He added: “We will have a chat as we normally would do but the boys know what’s expected of them. You don’t get league medals in December and January, they are handed out in May so there is a long, long way to go.
“Celtic know that as well. Neil [Lennon] will not be sitting saying ‘That’s us got the title’ — of course he won’t. We are both intelligent enough to know there is a lot of football to be played.”
While demanding a collective improvement from his team, McCoist refused to criticise individual players.
He said: “When your results aren’t what they were, it’s your job to dissect and look at the reasons for that.
“It would be wrong of me to sit here and criticise individuals in my team and I won’t do that at all.
“But I would say, collectively as a team, we haven’t been playing as well as we were doing earlier on in the season. I don’t think there is any doubt about that.
“There are parts of the season where individual performances will go up and down.
“It happens with every team. I won’t criticise any of my players individually but, as a team, we can do better.”
With top goalscorer Nikica Jelavic already linked with a January move to the Barclays Premier League, McCoist warned his players against allowing transfer speculation to act as a distraction.
He said: “That would be a concern but you hope that’s not the case.
“You just hope they are professional enough to know they have got a job to do.”